How to select a face created with edges?
Those black lines are edges which are co-planar to that face, but not associated with it. If you select those edges, they can be deleted without deleting the face. If you want to select those face sections individually, you'll have to remake them first. Start by deleting the face. Then select the edges (or verts) around one of the desired faces, then press 'F' to generate a new face there. Hope this helps!